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<title>Covariance Matrix Fusion</title>
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<h1>Covariance Matrix Fusion</h1>
<div id="subtitle"><a href="mailto:manuelgr@stanford.edu">Manuel Gomez Rodriguez</a>, <a href="mailto:robert.henriksson@stanford.edu">Robert Henriksson</a>, and <a href="mailto:rigtorp@stanford.edu">Erik Rigtorp</a></div>
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<h2>Abstract</h2>
<p>We consider the problem of estimating a positive semidefinite (PSD) matrix <img class="eq" src="eqs/2034097362-130.png" alt="S" style="vertical-align: -1px" /> that best fits a set of given PSD symmetric submatrices under 
some convex similarity measure, and some bounds 
on linear functions of <img class="eq" src="eqs/2034097362-130.png" alt="S" style="vertical-align: -1px" />. This can be formulated as a convex optimization problem.
The quality of estimation for every element of the matrix <img class="eq" src="eqs/2034097362-130.png" alt="S" style="vertical-align: -1px" /> is considered equally important and therefore, 
different entry-wise norms are 
proposed as similarity measures (i.e., Frobenius norm, <img class="eq" src="eqs/1502088427-130.png" alt="l_{1}" style="vertical-align: -3px" /> norm). The dual formulation is discussed under Frobenius norm 
assumption. Furthermore, different 
stochastic formulations are explored. One application we consider is the estimation of the covariance matrix 
for the daily return of a collection of stocks given a set of estimated covariance 
submatrices from different sources. Performance of the 
estimation will be discussed for different constraints and availability of data.</p>
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<h2>Results</h2>
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<ul>
<li><p><a href="final_report.pdf">Final Report</a></p>
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<li><p><a href="code/">Code</a></p>
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